THE RELATIVE SIGNIFICANCE OF SYNTACTIC KNOWLEDGE AND VOCABULARY KNOWLEDGE IN SECOND LANGUAGE LISTENING COMPREHENSION

The main purpose of the current study was to examine the role of vocabulary knowledge (VK) and syntactic knowledge (SK) in L2 listening comprehension, as well as their relative significance. Unlike previous studies, the current project employed assessment tasks to measure aural and proceduralized VK and SK. In terms of VK, to avoid under-representing the construct, measures of both breadth (VB) and depth (VD) were included. Additionally, the current study examined the role of VK and SK by accounting for individual differences in two important cognitive factors in L2 listening: metacognitive knowledge (MK) and working memory (WM). Also, to explore the role of VK and SK more fully, the current study accounted for the negative impact of anxiety on WM and L2 listening. The study was carried out in an English as a Foreign Language (EFL) context, and participants were 263 Iranian learners at a wide range of English proficiency from lower-intermediate to advanced. Participants took a battery of ten linguistic, cognitive and affective measures. Then, the collected data were subjected to several preliminary analyses, but structural equation modeling (SEM) was then used as the primary analysis method to answer the study research questions. Results of the preliminary analyses revealed that MK and WM were significant predictors of L2 listening ability; thus, they were kept in the main SEM analyses. The significant role of WM was only observed when the negative effect of anxiety on WM was accounted for. Preliminary analyses also showed that VB and VD were not distinct measures of VK. However, the results also showed that if VB and VD were considered separate, VD was a better predictor of L2 listening success. The main analyses of the current study revealed a significant role for both VK and SK in explaining success in L2 listening comprehension, which differs from findings from previous empirical studies. However, SEM analysis did not reveal a statistically significant difference in terms of the predictive power of the two linguistic factors. Descriptive results of the SEM analysis, along with results from regression analysis, indicated to a more significant role for VK.

Quantitative Derivation of Effective Evolution Equations for the Dynamics of Bose-Einstein Condensates

This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.